# 21-241: Matrix Algebra

### Schedule and Homework

For each week there will be a link to a page with a reading assignment and a homework assignment.

This schedule is tentative. It will get more accurate as the semester progresses. As each topic is covered in lecture, the color will be changed from blue to black.

 Week #1:  Jan 10 - 14 Homework 1.1. Systems of Linear Equations. 1.2. Row Reduction and Echelon Forms. 1.3. Vector Equations. Week #2:  Jan 17 - 21 Homework 1.4. The Matrix Equation Ax = b. 1.5. Solution Sets of Linear Systems. 1.7. Linear Independence. Administrative Note: Monday 17 January is Martin Luther King Day. Class will meet. Week #3:  Jan 24 - 28 Homework 1.8. Introduction to Linear Transformations. 1.9. The Matrix of a Linear Transformation. 2.1. Matrix Operations. Week #4:  Jan 31 - Feb 4 Homework 2.2. The Inverse of a Matrix. 2.3. Characterizations of Invertible Matrices. 2.5. Matrix Factorizations. Week #5:  Feb 7 - 11 Homework 2.7. Applications to Computer Graphics. 3.1. Introduction to Determinainants. Administrative Note: Monday 7 February is the Mid-Mini Break. Class will not meet. Week #6:  Feb 14 - 18 Homework 3.2. Properties of Determinants. 4.1. Vector Spaces and Subspaces. Exam #1 will be given on Wednesday 16 February. The exam will be held during your regular class time. Here are some review problems. Week #7:  Feb 21 - 25 Homework 4.2. Null Spaces, Column Spaces, and Linear Transformations. 4.3. Linearly Independent Sets; Bases. 4.4. Coordinate Systems. Week #8:  Feb 28 - Mar 4 Homework 4.5. The Dimension of Vector Space. 4.6. Rank. Administrative note: Friday 4 March is the Mid-Semester Break. Class will not meet. Mar 7 - 11 Spring Break. Week #9:  Mar 14 - 18 Homework 4.7. Change of Basis. 4.9. Applications to Markov Chains. 5.1. Eigenvectors and Eigenvalues. Week #10:  Mar 21 - 25 Homework 5.2. The Characteristic Equation. 5.3. Diagonalization. Exam #2 will be given on Wednesday 23 March. Here are some review problems. Week #11:  Mar 28 - Apr 1 Homework 5.4. Eigenvectors and Linear Transformations. 5.5. Complex Eigenvalues. 5.6. Discrete Dynamical Systems. Week #12:  Apr 4 - 8 Homework 6.1. Inner Product, Length, and Orthogonality. 6.2. Orthogonal Sets. 6.3. Orthogonal Projections. Week #13:  Apr 11 - 15 Homework 6.4. The Gram-Schmidt Process. 6.5. Least-Squares Problems. Administrative Note: Friday 15 April is the Spring Carnival break. Class will not meet. Week #14:  Apr 18 - 22 Homework 7.1. Diagonalization of Symmetric Matrices. 7.2. Quadratic Forms. Exam #3 will be given on Wednesday 20 April. Here is a study guide. Week #15:  Apr 25 - 28 7.4. The Singular Value Decomposition. 7.5. Applications to Image Processing and Statistics. 2.4. Partitioned Matrices. Administrative note: Friday 28 April is the last day of class. Final Exam May 9 Final Exam. Our final exam has been scheduled for Monday 9 May from 5:30-8:30pm. When scheduling your departure, do not plan to leave before May 10. Early exams will not be given. Here are some review problems.

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